The following random sample was selected from a normal distr

The following random sample was selected from a normal distribution: 5, 8, 4, 6, 10, 3. Construct a 95% confidence interval for the population mean

Solution

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    6          
t(alpha/2) = critical t for the confidence interval =    2.570581836          
s = sample standard deviation =    2.607680962          
n = sample size =    6          
df = n - 1 =    5          
Thus,              
              
Lower bound =    3.263406661          
Upper bound =    8.736593339          
              
Thus, the confidence interval is              
              
(   3.263406661   ,   8.736593339   ) [ANSWER]